# semirings: two monoids as one, in holy haskimony

Haskellers are usually familiar with monoids and semigroups. A monoid has an appending operation `<>`

(or `mappend`

),
and an identity element, `mempty`

. A semigroup has an appending `<>`

operation, but does not require a `mempty`

element.

A Semiring has two appending operations, `plus`

and `times`

, and two respective identity elements, `zero`

and `one`

.

More formally, a Semiring R is a set equipped with two binary relations `+`

and `*`

, such that:

(R,+) is a commutative monoid with identity element 0,

(R,*) is a monoid with identity element 1,

(*) left and right distributes over addition, and

multiplication by `0`

annihilates R.

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Versions [faq] | 0.0.0, 0.1.0, 0.1.1, 0.1.2, 0.1.3.0, 0.2.0.0, 0.2.0.1, 0.2.1.0, 0.2.1.1, 0.3.0.0, 0.3.1.0, 0.3.1.1, 0.3.1.2, 0.4, 0.4.1, 0.4.2, 0.5, 0.5.1, 0.5.2, 0.5.3 |
---|---|

Change log | CHANGELOG.md |

Dependencies | base (>=4.5 && <5), containers (>=0.5.4 && <0.7), hashable (>=1.1 && <1.4), integer-gmp, nats (>=0.1 && <2), semigroups (>=0.17), tagged, transformers, unordered-containers (==0.2.*) [details] |

License | BSD-3-Clause |

Copyright | Copyright (C) 2018 chessai |

Author | chessai |

Maintainer | chessai <chessai1996@gmail.com> |

Category | Algebra, Data, Data Structures, Math, Maths, Mathematics |

Home page | http://github.com/chessai/semirings |

Bug tracker | http://github.com/chessai/semirings/issues |

Source repo | head: git clone git://github.com/chessai/semirings.git |

Uploaded | by chessai at 2020-02-18T19:39:38Z |

Distributions | LTSHaskell:0.2.1.1, NixOS:0.5.3, Stackage:0.4.2 |

Downloads | 8076 total (597 in the last 30 days) |

Rating | 2.0 (votes: 1) [estimated by Bayesian average] |

Your Rating | |

Status | Docs available [build log] Last success reported on 2020-02-18 [all 1 reports] |

## Modules

[Index] [Quick Jump]

## Flags

Name | Description | Default | Type |
---|---|---|---|

hashable | You can disable the use of the Disabling this may be useful for accelerating builds in sandboxes for expert users. Note: | Enabled | Manual |

containers | You can disable the use of the Disabling this may be useful for accelerating builds in sandboxes for expert users. | Enabled | Manual |

unordered-containers | You can disable the use of the Disabling this may be useful for accelerating builds in sandboxes for expert users. | Enabled | Manual |

Use -f <flag> to enable a flag, or -f -<flag> to disable that flag. More info

## Downloads

- semirings-0.5.3.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)